Evaluate:` 1 - ((5)/(-7)) -(3)/(14)`

Answer

To evaluate the expression \( 1 - \left( \frac{5}{-7} \right) - \frac{3}{14} \), we will follow these steps:

### Step 1: Rewrite the expression
The original expression is:
\[ 1 - \left( \frac{5}{-7} \right) - \frac{3}{14} \]
Since the fraction \( \frac{5}{-7} \) has a negative sign in the denominator, we can move the negative sign to the numerator:
\[ 1 + \frac{5}{7} - \frac{3}{14} \]

### Step 2: Convert 1 to a fraction
To perform the addition and subtraction, we need a common denominator. We can express 1 as a fraction:
\[ 1 = \frac{1}{1} = \frac{14}{14} \]
So now our expression looks like:
\[ \frac{14}{14} + \frac{5}{7} - \frac{3}{14} \]

### Step 3: Convert \( \frac{5}{7} \) to have a common denominator
The denominator of \( \frac{5}{7} \) needs to be converted to 14. We can do this by multiplying both the numerator and the denominator by 2:
\[ \frac{5}{7} = \frac{5 \times 2}{7 \times 2} = \frac{10}{14} \]

### Step 4: Substitute back into the expression
Now we can substitute \( \frac{10}{14} \) back into the expression:
\[ \frac{14}{14} + \frac{10}{14} - \frac{3}{14} \]

### Step 5: Combine the fractions
Now that all fractions have the same denominator, we can combine them:
\[ \frac{14 + 10 - 3}{14} = \frac{21}{14} \]

### Step 6: Simplify the fraction
Now we can simplify \( \frac{21}{14} \):
\[ \frac{21 \div 7}{14 \div 7} = \frac{3}{2} \]

### Final Answer
Thus, the evaluated expression is:
\[ \frac{3}{2} \]

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